# Anyone have experience with payback calculations?

| Posted in Energy Efficiency and Durability on

I had an energy audit yesterday, and they claimed I could get a 5 year payback by adding more attic insulation. I found a payback calculation online, and that came back with 30 years. I want to do the right thing, but it also needs to make financial sense. Anyone have experience with the payback calculation? I put my specifics in the “more explanation” section. Did I do it correctly? Hoping to find someone smarter than me (that part won’t be hard) to help. Thanks.
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Current insulation is R30 – fiberglass
Wanting to add insulation to bring it up to R49 (improvement of R19)
– Insulation quote is \$1,552 for 2,004 square feet or \$0.774 / sq ft
My furnace is 96% efficient
My gas bill is \$0.64 / CCF for natural gas, or \$0.00000621 per BTU
My electricity bill is \$0.16566 per KwH or \$0.0000485 per BTU (summer premium)
I live near Muskegon Michigan, so we have 6,420 Heating degree days and 791 cooling degree days

So the calculation as I understand it should be:
(\$0.77 x 30 x 49 x 96%) / (((6,420 x \$.00000621) + (791 x \$.0000485)) x (49 – 30) x 24)

1,087 / (.03987 + .03836) x 19 x 24

1,087 / 35.67 = 30 years

Is that correct?

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### Replies

1. Expert Member
| | #1

Throwing around a bunch of numbers with no units on them makes it difficult or impossible to follow, but whatever that reckoning you have up there is, it ain't right.

The 96% combustion efficiency of the furnace is only part of the total system efficiency- you need to factor in the duct losses, air handler driven infiltration and the power used by the air handler, etc., so anything based on just 96% AFUE is optimistic at best.

That said, let's take a stabe at it, hanging enough verbiage on it to know what the hell the numbers really mean.

The heat loss per square hour per square foot per degree of difference is the inverse of the R-value. (That's the most basic definition of R-value.)

Assuming (against reason) that the attic temp is always pretty close to the outdoor ambient (which it totally ISN'T, even if well-ventilated), and that your ceiling temp averaged 65F (the heating degree-day base number- probably a bit on the low side, eh?) given 6420 heating degree-days, with 24 hours in a day, is 6420 x 24= 154,080 degree-hours.

With R30 the annual heat loss per square foot is 154,080/30= 5136 BTU per square foot.

With R49 the annual heat loss per square foot is 54,080/49= 3144 BTU per square foot.

That means you're saving about 1992 BTU per square foot per year with that upgrade.

The BTU per CCF varies with the gas mix on your local grid. From your arithmetic it looks like you're assuming (or have local utility information) indicating 103,000 BTU/ccf . In a 96% burner in your perfect zero duct loss system (that uses no electricity) and zero infiltration home, that means you're getting 0.96 x 103= 98,880 BTU per ccf.

That means the upgrade is saving you 1992/98,880 = 0.201 CCF per year per square foot.

Assuming zero fuel inflation, and zero interest on the cash, you'll be saving 0.2 x \$0.64=\$ 0.129 per square foot per year.

If it cost you \$0.774 for that square foot, the the simple payback is \$0.774/\$ 0.129 = 6.0years.

That's not 5 years, but it's a lot closer to 5 than it is to 30.

Your actual ceiling temps is probably higher than 65F, but so is your average attic temp, due to direct solar gains on the roof when it isn't covered with snow, and the insulting effects of the snow when it IS covered. But let's call it a wash for now- without a lot more information we don't have a basis for making up a correction factor.

Real duct systems and real houses leak air, and rare is the ducted air system that isn't losing at least 10% to duct leakage + air handler driven infiltration, and we haven't factored in the air handler power use, OR the air-conditioning power savings, so in reality, it probably really IS about a 5 year simple payback.

Do you know of any other investments with an IRR in the 17-20% range, that pays off tax free, and is both safe & legal?

2. GBA Editor
| | #2

Greg,
Dana has done a good job providing feedback.

There are two aspects to your question. The first concerns heat-loss calculations. The second concerns payback calculations.

3. | | #3

Thanks Dana

It makes sense when you know what the numbers represent. I couldn't figure out what he was doing. But shouldn't the CCF be 0.0201, or am I missing something?

Andy

4. Expert Member
| | #4

The content of natural gas varies by local-grid inputs- it's not pure methane. A typical number is 100- 102,000 BTU/CCF but it can be as high a 105,000, or even higher. If it's almost pure methane with a still-legally pipeline-able amount of CO2 content (like some coal seam gas) it can be as low as 80-85,000 BTU/CCF. The actual BTU content per CCF delivered by the local gas-grid operator varies, an often appears on the billing.

Mine is usually somewhere in the 102 K & change range, and I'm billed by the heat content, not the CCF, since the heat content varies depending on what came down the pipeline or on the LNG tanker most recently. If you take Greg's \$0.64 per CCF and divide by his \$0.00000621 per BTU you end up with 103,059.6 BTU/CCF, which is a credible number, but higher than typical on my local grid, and way above pure (or CO2 contaminated) methane.

5. | | #5

Mine was a decimal point question. I think it is .02 instead of 0.2

6. | | #6

Is the insulator proposing to insulate the attic further without air-sealing it?

7. | | #7

I think Andy's on to something with that missing decimal point. It would be very hard to save \$300+/year going from R30 to R50, even in Michigan. At the quoted prices, that would be ~500 CCF saved per year. Spread over 2000 sq ft, that's .25 CCF/sq ft. At 100,000 BTU/CCF, that would require saving 25,000 BTU/sq ft. With 150,000 degree-hours of heating, this would require going from R6 to Rinf (150K/6 = 25K). Starting at R30, it's not going to happen.

Greg --- Unless your attic is actually starting at something less than R5, your suspicion is well founded. I'm sure you've already seen it, but the numbers here (http://energy.gov/energysaver/articles/estimating-payback-period-additional-insulation) are worth comparing to your situation. In their worked example, with a higher fuel cost and at 1/5 the cost for insulation they calculated a 5 year payback for going from R20 to R30 in a similar climate. Did the audit happen to be conducted by the same people who quoted you on installing the insulation?

8. | | #8

Thanks so much for all of the helpful input. I feel a rather embarrassed about giving all of the numbers to a calculation without citing the formula or giving you links to where I found it. Very thankful you were able to fight through it.

The insulation quote and initlal (subjective) payback info all came from the audit company. Based on conversations with another insulation contractor, I don't think the insulation cost is out of line. However the discussion around the benefits seems to be significantly overstated.

I really appreciated Nathan's comment as it provided a very practical example in addition to all of the formulas. Taking a step back and looking at the situation at a high level was very helpful. Saving \$300 / year is very unlikely, especially since I have a good base of insulation already. That validates the calculations.

Thanks to all for the assistance!

9. Expert Member
| | #9

What effect does dropping the zero have? (Mea culpa- order of magnitude error- need more coffee, or more sleep, no question about it! :-) )

So, it's saving 1.3 cents per square foot of gas usage per year, which takes quite a bit of time to pay off the 77.4 cents/foot at zero energy inflation. Even if you bump that to 1.5 cents as the fudge-factor to account for power use and system efficiency it's on the order of 5 decades.

If the existing insulation is low-density fiberglass batts with the typical gaps & compressions and no top-side air barrier, if the new stuff is cellulose the performance boost would be considerably more than the simple math implies since the as-installed R-value of the pre-existing goods would be well below the labeled performance. With an overtopping of a more air-retardent insulation that also fills in the gaps & compressions it "restores" the performance of the low density goods by blocking the parasitic convection between the entrained air in the batts and the cool attic air.

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